Hi there,

"

If *k* is an integer and 5^*k* < 20,000, what is the greatest possible value of *k*?

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10

"

Intuitively I though I should turn 20,000 into 2^5 * 5^4, and since 2^5 is 32, k shouldn’t exceed 6 if 5^*k* is to be less than 20,000. However, even though I was able to find the correct choice, I still can’t articulate why this question can be solved in this way. I can’t breakdown the question and figure out what the question is asking in essence. Can anyone help me lay out a clearer thought process for solving this?

Thank you!